As an apparatus for controlling a transmission having a lockup function, there has been suggested an apparatus for setting a lockup area on the basis of a lockup line defined by a vehicle speed and a throttle opening degree (e.g. refer to a patent document 1). According to the apparatus disclosed in the patent document 1, the lockup is performed in an area in which the torque variation of an engine is not large and in which there is no booming noise even in the lockup.